The notion of homotopy relative Rota-Baxter Lie algebras was introduced by Lazarev, Sheng, and Tang [1]}. Homotopy theory of relative Rota-Baxter associative algebras is studied in [2]}. Roughly, a homotopy relative Rota-Baxter (associative) algebra is a triple consisting of an \(A_\infty \) -algebra, a bimodule over the \(A_\infty \) -algebra and a homotopy relative Rota-Baxter operator. In this section, we mainly focus on homotopy relative Rota-Baxter algebras whose underlying \(A_\infty \) -algebra and the bimodule are both concentrated in degrees 0 and 1. We call them 2-term homotopy relative Rota-Baxter algebras. We classify `skeletal' homotopy relative Rota-Baxter algebras.
